Q.

Light of wavelength 5.0 x 10-7 m  falls on a pair of narrow slits separated by a distance (2d). The interference pattern on a screen placed 2.0 m away shows that there is darkness at the position exactly opposite to each  slit. The separation between the slits

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a

0.5 mm

b

1.0 mm

c

2.0 mm

d

5×10−7 mm

answer is B.

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Detailed Solution

we know that β=λD2dHere, tho distance between two dark fringes is equal to the separation between the slits i.e β =2d(2d)=λD(2d)  or  (2d)2=λD or (2d)=(λD) so (2d)=5⋅0×10−7×2⋅01/2=10−3m=1⋅0mm
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Light of wavelength 5.0 x 10-7 m  falls on a pair of narrow slits separated by a distance (2d). The interference pattern on a screen placed 2.0 m away shows that there is darkness at the position exactly opposite to each  slit. The separation between the slits